Mathematics and Beauty : Aesthetic Approaches to Teaching Children

by Sinclair, Nathalie; Higginson, William

• ISBN13: 9780807747223
• ISBN10: 080774722X
• Format: Paperback
• Copyright: 2006-08-30
• Publisher: Teachers College Pr

Summary

In this innovative book, Nathalie Sinclair makes a compelling case for the inclusion of the aesthetic in the teaching and learning of mathematics. Using a provocative set of philosophical, psychological, mathematical, technological, and educational insights, she illuminates how the materials and approaches we use in the mathematics classroom can be enriched for the benefit of all learners. While ranging in scope from the young learner to the professional mathematician, there is a particular focus on middle school, where negative feelings toward mathematics frequently begin. Offering specific recommendations to help teachers evoke and nurture their students' aesthetic abilities, this book: Features powerful episodes from the classroom that show students in the act of developing a sense of mathematical aesthetics. Analyzes how aesthetic sensibilities to qualities such as connectedness, fruitfulness, apparent simplicity, visual appeal, and surprise are fundamental to mathematical inquiry. Includes examples of mathematical inquiry in computer-based learning environments, revealing some of the roles they play in supporting students' aesthetic inclinations. Book jacket.

Author Biography

Nathalie Sinclair is an assistant professor in the Department of Mathematics at Michigan State University.

Table of Contents

Foreword	p. vii
Acknowledgments	p. xi
Introduction	p. 1
Where Beautiful Mathematics Comes From	p. 1
The Aesthetic as a Vital Lens on Learning	p. 4
Plan for the Book	p. 9
A Background Note	p. 12
Beauty and Pleasure in Human Experience
Reclaiming the Aesthetic from the Arts	p. 17
The Fluidity of Human Faculties	p. 17
The Aesthetic Nature of Inquiry	p. 21
Connecting the Aesthetic to Learning: First Steps	p. 26
Fitting the Pieces Together	p. 28
"Wired" for Beauty and Pleasure	p. 29
Homo Aestheticus	p. 29
A "Sense of Order"	p. 33
Beauty and Pleasure in Mathematics
Developing a Mathematical Aesthetic Lens	p. 39
The Aesthetic	p. 39
The Mathematical Aesthetic	p. 42
The Mathematical Aesthetic in Action	p. 43
The Aesthetics of Detachment	p. 56
Aesthetics and the Development of Mathematics	p. 59
Debriefing the Kissing Triangles	p. 59
The Importance of the Mathematical Aesthetic	p. 61
Fitting the Pieces Together	p. 65
Focusing the Aesthetic Lens On Students
The Motivational Role of the Aesthetic	p. 69
The Aesthetic Dimension of Problem Selection	p. 71
The Aesthetic Dimension of Problem Posing	p. 74
Coloring with Numbers	p. 83
Fitting the Pieces Together	p. 97
The Generative Role of the Aesthetic	p. 99
Three Examples of the Generative Role	p. 100
Mindful Mathematics	p. 108
Fitting the Pieces Together	p. 109
The Evaluative Role of the Aesthetic	p. 113
Which Solution Is Better?	p. 117
Wonder and the Aesthetic	p. 129
Valuing the Aesthetic	p. 131
Fitting the Pieces Together: Aesthetics and Inquiry	p. 133
Aesthetic Enculturation
Peering Inside the Mathematics Culture	p. 139
From Outside to Inside the Culture	p. 139
What Do Mathematicians Value?	p. 140
The Aesthetic Dimension of Mathematical Values	p. 144
Mathematical Values in Teaching	p. 153
Revealing Values in Topics, Tasks, and Tools	p. 154
Communicating Values in the Classroom	p. 162
Some Closing Words	p. 175
Notes	p. 177
References	p. 183
Index	p. 191
About the Author	p. 196
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